Percent Change: Definition, Formula & Examples

Definitionnoun phrase

What is percent change in math?

Percent change measures how much a value grew or shrank relative to where it started: the difference divided by the original amount, written as a percent. From 50 to 60 is a 20% increase; from 80 to 60 is a 25% decrease. The original value is always the base, which is the step people get wrong.

In Spanish: cambio porcentual
Also called: percent increase, percent decrease, percentage change, relative change
Grade level: 6-8

Grade 7Grade 8Algebra 1CCSS 7.RP.A.3GEDSATACT

Percent Change in a picture

The change is 15 both times, but the base is different: 15 is a quarter of 60 (25% increase) and only a fifth of 75 (20% decrease).

Formal definition and notation

If a quantity changes from an original value a, with a ≠ 0, to a new value b, the percent change is b − aa × 100%. A positive result is a percent increase; a negative result is a percent decrease, usually reported as a positive number with the word decrease. Because the base is always the original value, a 25% decrease followed by a 25% increase does not return to the start. Markups, discounts, sales tax, tips and percent error are all percent-change problems.

Symbol	Read it as	Meaning
b − aa	new minus original, over original	the change as a fraction of the starting value
+20%	plus twenty percent	a 20% increase; −20% means a 20% decrease
× 1.2	times one point two	the multiplier for a 20% increase; × 0.8 is the multiplier for a 20% decrease

Key facts

A 20% increase multiplies by 1.2, and a 20% decrease multiplies by 0.8, so you can find the new value in one step.
Up and then down by the same percent is a net loss: 100 rises 25% to 125, then falls 25% to 93.75.
An increase can be more than 100% (50 to 150 is a 200% increase), but a decrease of a positive amount can be at most 100%.
Percentage points are different: a rate going from 40% to 50% rose 10 percentage points, which is a 25% increase.
Percent error has the same shape: |measured − actual|actual × 100%.

Percent change formula

percent change = new − originaloriginal × 100%

original: the starting value: the base you divide by
new: the value after the change
new − original: the amount of change: positive for an increase, negative for a decrease

Positive answer: increase. Negative answer: decrease. To apply a change instead, multiply by 1 + p100 for a p% increase or 1 − p100 for a decrease.

Percent Change examples, step by step

Example 1: A percent increase

Warm-up

A movie ticket costs 25 dollars last year and 30 dollars this year. What is the percent change?

Change: 30 − 25 = 5 dollars.
Divide by the original price: 525 = 0.2.
Write as a percent: 0.2 × 100 = 20. The change is positive, so it is an increase.

Answer: The price rose by a 20% increase.

Example 2: A percent decrease

Core

A school’s lunch waste fell from 640 pounds a week to 528 pounds a week. What is the percent change?

Change: 528 − 640 = −112 pounds.
Divide by the original amount: −112640 = −0.175.
Multiply by 100: −17.5. Negative means a decrease.

Answer: The waste went down by a 17.5% decrease.

Example 3: Two changes in a row

Test-style

A store raises a price by 20%, then puts the new price on sale for 20% off. What is the overall percent change from the original price?

A 20% increase multiplies by 1.2, and a 20% decrease multiplies by 0.8.
Overall multiplier: 1.2 × 0.8 = 0.96.
0.96 is 96% of the original, so the price is 4% lower.
The two 20% changes do not cancel, because the second one is taken of a larger base.

Answer: The overall change is a 4% decrease.

Common mistakes

✗ Mistake80 to 60: the change is 20, and 20 ÷ 60 ≈ 33%, so a 33% decrease.

✓ Instead20 ÷ 80 = 0.25: a 25% decrease.

Use the original value in the denominator, not the new value.

✗ Mistake50 to 60 is a 10% increase, because it went up 10.

✓ Instead1050 = 0.2: a 20% increase.

The amount of change is not the percent change. Divide the change by the original value first.

✗ MistakeA 25% increase followed by a 25% decrease brings a price back to where it started.

✓ Instead100 becomes 125, then 125 × 0.75 = 93.75: a 6.25% overall decrease.

The second percent is taken of the new, larger value, so it removes more than the first one added.

✗ MistakeAn interest rate went from 4% to 5%, a 1% increase.

✓ InsteadIt rose 1 percentage point, which is a 25% increase (14 = 0.25).

When the values are already percents, say percentage points for the simple difference.

Not to be confused with

Percent Changevs.Percent

A percent describes a part of one whole: 15 is 25% of 60. Percent change compares two values over time: 60 to 75 is a 25% increase.

Percent Changevs.Percentage points

Percentage points are a plain difference of two percents: 40% to 50% is up 10 points. Percent change divides that difference by the start: a 25% increase.

Percent Changevs.Percent error

Percent error compares a measured or estimated value with the true value, and divides by the true value. It is reported without a sign.

Quick check: 3 questions

Question 1 of 3

A plant grows from 12 cm to 15 cm. What is the percent increase?

Show answer and explanation

Answer: C. Change = 3 cm, and 312 = 0.25 = 25%. Choice A gives the amount of change, B divides by the new height, and D is the new height as a percent of the old one.

Question 2 of 3

A 90-dollar jacket goes on sale for 63 dollars. What is the percent decrease?

Show answer and explanation

Answer: A. Change = 27 dollars, and 2790 = 0.3 = 30%. Choice B is the dollar change, C is the sale price as a percent of the original, and D divides by the sale price.

Question 3 of 3

A value increases by 50%, and then the new value decreases by 50%. What is the overall change?

Show answer and explanation

Answer: B. 1.5 × 0.5 = 0.75, so the final value is 75% of the start: a 25% decrease. The changes do not cancel, because the 50% decrease is taken of the larger value.

Percent Change: frequently asked questions

How do you calculate percent change?

Subtract the original value from the new value, divide by the original value, and multiply by 100. From 40 to 46: 46 − 40 = 6, 640 = 0.15, so the change is a 15% increase. If the result is negative, the value decreased. Always divide by the value you started with.

Can percent change be more than 100%?

An increase can. From 20 to 50 the change is 30, and 3020 = 1.5, a 150% increase; doubling is a 100% increase. A decrease of a positive quantity cannot pass 100%, because a 100% decrease already takes the value down to 0.

What is the difference between percent change and percentage points?

Use percentage points for the plain difference between two percents and percent change for the relative difference. If a test pass rate rises from 60% to 75%, it rose 15 percentage points. As a percent change it rose 1560 = 25%. News reports often mix these up, so check which one is meant.

Practice and tools

Effortless Math practicePractice on Effortless Math Percent Change CalculatorPercent increase or decrease between two values, with steps Discount, Tax and Tip CalculatorApply a percent change to a price Percentage CalculatorPercent of a number and reverse percent problems

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.RP.A.3

Cite this entry

Effortless Math Team. “Percent Change.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/percent-change/

Flashcard

TermPercent Change(new − original) ÷ original

DefinitionHow much a value grew or shrank compared with where it started. From 50 to 60: 10 ÷ 50 = 20% increase.

Study the full deck

Browse all terms in the Math Dictionary · More ratios and proportions terms · Random term

Percent IncreasePercent increase is how much a quantity grew, written as a percent of its original value. Subtract the original from the new value, divide by the original, and multiply by 100: from 80 to 100 is 2080 = 25%. To increase a number by r%, multiply it by 1 + r100, so 80 × 1.25 = 100.Ratios and Proportions · Grade 7, Grade 8, Algebra 1Percent DecreasePercent decrease is how much a quantity went down, written as a percent of its original value. Subtract the new value from the original, divide by the original, and multiply by 100. A price that drops from 80 dollars to 60 dollars has a decrease of 20 dollars, and 2080 = 25%.Ratios and Proportions · Grade 7, Grade 8, Algebra 1NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5DifferenceA difference is the result of subtracting one number from another. In 12 − 7 = 5, the difference is 5. It tells how much bigger one number is than another, or how far apart they are on a number line. “The difference of a and b” means a − b, in that order.Operations · Grade 1, Grade 2, Grade 3PercentA percent is a number out of 100. Percent means per hundred, so 25% means 25 out of 100, or 25100 = 0.25. To find a percent of a quantity, change the percent to a decimal and multiply: 20% of 80 is 0.20 × 80 = 16. The symbol for percent is %.Number System · Grade 5, Grade 6, Grade 7RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8ProportionA proportion is an equation that says two ratios are equal, such as 12 = 36. It is read 1 is to 2 as 3 is to 6. In a true proportion the cross products are equal, which lets you find a missing value. Proportions are often used to solve scale, percent, and rate problems.Ratios and Proportions · Grade 6, Grade 7, Grade 8Simple InterestSimple interest is interest paid only on the original amount of money, called the principal, at a fixed yearly rate. Find it with I = Prt: multiply the principal by the rate written as a decimal and by the time in years. The interest is the same every year, so the balance grows in a straight line.Ratios and Proportions · Grade 7, Algebra 1Exponential GrowthExponential growth is an increase by the same percent, or the same factor, in each equal time period, so the amount grows faster and faster. It is modeled by y = a(1 + r)^t, where a is the starting amount and r is the growth rate. Growing 10% a year multiplies the amount by 1.1 every year.Functions · Algebra 1, Algebra 2Unit RateA unit rate is a rate that compares a quantity to one unit of another quantity, such as 50 miles per hour or 4 dollars per notebook. To find it, divide the first quantity by the second: 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour. The word per means for each one.Ratios and Proportions · Grade 6, Grade 7, Grade 8

Percent Change

What is percent change in math?

Percent Change in a picture

Formal definition and notation

Key facts

Percent change formula

Percent Change examples, step by step

Example 1: A percent increase

Example 2: A percent decrease

Example 3: Two changes in a row

Common mistakes

Not to be confused with

Quick check: 3 questions

Percent Change: frequently asked questions

How do you calculate percent change?

Can percent change be more than 100%?

What is the difference between percent change and percentage points?

Related terms

Practice and tools

Sources

Flashcard

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